The Li–Wan sieve [11] is extended to multisets when the underlying set symmetric. main ingredient of proof Möbius inversion formula on poset partitions {1,2,…,k} ordered by refinement. As illustrative applications, we investigate problems over finite fields and zero-sum additive group Z/nZ.

A homomorphic, or incremental, multiset hash function, associates a hash value to arbitrary collections of objects (with possible repetitions) in such a way that the hash of the union of two collections is easy to compute from the hashes of the two collections themselves: it is simply their sum under a suitable group operation. In particular, hash values of large collections can be computed inc...

The paper delineates the problem related to difference and complementation in Multiset Theory. It is shown that none of the existing approaches succeeds in resolving the attendant difficulties without assuming some contrived stipulations. Mathematics Subject Classifications: 03E15, 03E20, 03E30

Local optimality conditions are given for a quadratic programming formulation of the multiset graph partitioning problem. These conditions are related to the structure of the graph and properties of the weights.

Eigenvalues of a graph are the eigenvalues of its adjacency matrix. The multiset of eigenvalues is called its spectrum. There are many properties which can be explained using the spectrum like energy, connectedness, vertex connectivity, chromatic number, perfect matching etc. Laplacian spectrum is the multiset of eigenvalues of Laplacian matrix. The Laplacian energy of a graph is the sum of the...

The aim of this research is to produce an algorithm for the software that would let a researcher to observe the evolution of maximally parallel multiset-rewriting systems with permitting and forbidding contexts, browsing the configuration space by following transitions like following hyperlinks in the World-Wide Web. The relationships of maximally parallel multiset-rewriting systems with other ...

In this paper we prove two multiset analogs of classical results. We prove a multiset analog of Lovász’s version of the Kruskal-Katona Theorem and an analog of the Bollobás-Thomason threshold result. As a corollary we obtain the existence of pebbling thresholds for arbitrary graph sequences. In addition, we improve both the lower and upper bounds for the ‘random pebbling’ threshold of the seque...